# Carbon dating differential equation

Carbon is naturally in all living organisms and is carbon in the tissues by eating other organisms or by breathing air that contains carbon.At any particular time all living organisms have approximately the same ratio carbon carbon 12 to carbon 14 carbon their tissues.However, as the object cools, the temperature difference gets smaller, and the cooling rate decreases; thus, the object cools more and more slowly as time passes.To formulate this process mathematically, let Example 4: A cup of coffee (temperature = 190°F) is placed in a room whose temperature is 70°F.For a sky diver falling in the spread‐eagle position without a parachute, the value of the proportionality constant stays constant.This occurs when the speed is low enough for the weight of the sky diver to balance the force of air resistance; the net force and (consequently) the acceleration reach zero.The amount at any time is given by, $$r(t) = Ce^$$ The amount at a later time $t \tau$ should be half as much (\tau is the half life).

The term orthogonal means perpendicular, and trajectory means path or cruve.

After five minutes, the temperature of the coffee has dropped to 160°F.

How many more minutes must elapse before the temperature of the coffee is 130°F?

Assuming that the coffee obeys Newton's Law of Cooling, its temperature amount of time after the coffee is initially placed in the room for its temperature to drop to 130°F.

Therefore, after waiting five minutes for the coffee to cool from 190°F to 160°F, it is necessary to then wait an additional seven minutes for it to cool down to 130°F. Once a sky diver jumps from an airplane, there are two forces that determine her motion: the pull of the earth's gravity and the opposing force of air resistance.

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